Although the classical computer (a computer based on classical physics) has evolved from a relatively large, low performance and expensive number cruncher to a compact, high performance and cost effective computing engine, the modern day classical computer is fundamentally no different from first generation classical computers. By way of example, today and yesterday's classical computers simply manipulate and interpret an encoding of binary bits to produce a useful computational result. In general, a binary bit is a fundamental unit that is classically represented as “0” or “1,” wherein a series of such bits can be utilized to encode information. The series of bits (or encoded information) generally is manipulated via Boolean logic (e.g., logic gates such as AND, OR, etc.) to produce useful results. This classical physics notion of a binary bit of information can be physically realized through a macroscopic physical system such as magnetization on a hard disk or charge on a capacitor.
Whereas the classical computer obeys the laws of classical physics, a quantum computer leverages physical phenomenon unique to quantum mechanics to render a new paradigm of information processing. In the quantum mechanics paradigm, the fundamental unit of information is a quantum bit, or qubit. With quantum computers, qubits are manipulated by executing a series of quantum gates, which are each a unitary transformation acting on a single qubit or pair of qubits. By applying quantum gates in succession, a quantum computer can perform a computationally complicated unitary transformation to a set of qubits in some initial state. Unlike the bit of classical physics, the qubit is not binary, but rather more quaternary in nature. This property arises as a consequence of its adherence to the laws of quantum mechanics, which substantially differ from the laws of classical physics. By way of example, a qubit can exist not only in a state corresponding to a logical state of “0” or “1,” like a classical bit, but additionally in states corresponding to a superposition of the classical states. Thus, a qubit can exist as “0,” “1,” or simultaneously as both “0” and “1,” with a numerical coefficient representing a probability for each state.
This notion of a superposition of states theoretically provides computational leaps (orders of magnitude) over the classical computer. By way of example, a quantum system of 500 qubits represents a quantum superposition of as many as 2500 states. In classical physics, these states essentially are equivalent to a single list of 500 “1's” and “0's.” Thus, any quantum operation on this quantum system would simultaneously operate on all 2500 states (state machines) with each clock cycle. This is essentially equivalent to performing the same operation on a classical computer employing ˜10150 separate processors. Thus, theoretically the quantum computer demonstrates superior computational power over the classical computer.